Relativistic second-order dissipative fluid dynamics at finite chemical potential

We employ a Chapman-Enskog like expansion for the distribution function close to equilibrium to solve the Boltzmann equation in the relaxation time approximation and subsequently derive second-order evolution equations for dissipative charge current and shear stress tensor for a system of massless quarks and gluons. We use quantum statistics for the phase space distribution functions to calculate the transport coefficients. We show that, the second-order evolution equations for the dissipative charge current and the shear stress tensor can be decoupled. We find that, for large chemical potential, the charge conductivity is small compared to the shear viscosity. Moreover, we demonstrate that the limiting behaviour of the ratio of heat conductivity to shear viscosity is identical to that obtained for a strongly coupled conformal plasma.